three cables are pulling on an object which is in static equilibrium. If 2 of the forces have the same magnitude but are separated by a 32 degree angle, determine the magnitude and direction of the third force.

Answer 1

Vector sum of F and F with an angle 32o between them is according to the cosine law
F12 =sqrt(F^2 + F^2 – 2•F^2•cos [(360 - 2•32)/2)]) =
=sqrt(2•F•(1-cos148)) =1.92•F
F3 =F12 = 1.92F (of opposite direction)